Copy Rotation Bone Constraint fails
First, yes it is supposed to happen. If it is expected or not depends on whether on not you have read this answer. :)  

The reason this happens is because bones in blender are not Z up like everything else, but the Y axis is up.

Here is a picture set up the same as yours, but with the axis display turned on for the armature.


You can easily "fix" the offset by changing the rotational space from World to Local with Parent. (You will in most cases want to use local with Parent space anyway.) 




Try rotating the bone in edit mode, then see what the constraint does with Offset turned on and the Space set to World. (Hint, you will end up needing Local with Parent.)